It has long been known that elements that shift the phase of an optical signal in response to an input signal are extremely useful for the control of optical signals, both as such and as components of more complex devices. For example, filters, switches, and modulators can all be constructed, at least in part, from phase-shifting elements.
Useful phase-shifting elements have been based on various underlying physical phenomena. Among these phenomena is the free-carrier effect in semiconductive optical media, whereby the refractive index of an optical medium at a given wavelength is dependent on the density of free carriers, i.e. of mobile electrons and/or holes, in the optical medium.
A free-carrier modulator can be implemented in silicon, whereby the application of a forward or reverse bias voltage modulates the carrier density in the region of a p-n junction. Changes in the carrier density lead to changes in the refractive index in the optical path, which lead, in turn, to modulation of the phase of the propagating optical signal.
A resonant free-carrier modulator can have a resonant frequency ωm that exhibits a shift Δωm which is proportional to ωm, with ωm further depending on an overlap between the change of the depletion width in the junction region and the energy distribution of the guided resonant optical mode. The depletion width, in turn, is controlled by a bias voltage applied across the junction. Accordingly, the same electrorefractive effect that modulates the refractive index can also be utilized to shift the resonant frequency of a device (whereby the resonant frequency can be a function of the refractive index), thus leading to applications in spectrally selective modulation and filtering.
As mentioned, refractive index can depend on carrier concentrations, Eqn. 1 provides an empirical expression for the refractive index change Δn in the junction region in silicon at a wavelength of 1550 nm:Δn=ANB+jCND  Eqn. 1where j2=−1, N is the electron or hole concentration, and the parameters A, B, C, and D are provided in the following table:
TABLE 1Refractive Index Change ParametersA (×10−24)BC (×10−24)DFor electrons−23.71.080.04921.2For holes−3,930,0000.821.961.1
An estimation of how a depletion width w can be varied by a voltage applied across a junction can be determined per Eqn. 2:
                    w        =                                                                              2                  ⁢                                                                          ⁢                  ɛ                                q                            ·                                                                    N                    A                                    +                                      N                    D                                                                                        N                    A                                    ⁢                                      N                    D                                                                                ⁢                      (                          V              +                              φ                B                                      )                                              Eqn        .                                  ⁢        2            where ∈ is the dielectric constant, q is the electronic charge, V is the applied voltage, φB is the built-in potential, and ND and NA are respectively the donor and acceptor concentrations.
Junction-based free-carrier modulators and similar devices have advantageous properties. However, the free-carrier effect for such devices is often weaker than other physical mechanisms for producing refractive index changes. Therefore, there remains a need for further enhancements in the effectiveness of junction-based free-carrier modulators and the like.